Is n an integer?

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gamecomplete: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Jun 07, 2015 10:55 pm; Thanked: 3 times

by gamecomplete » Sun Jun 07, 2015 10:58 pm

Is n an integer?

(1) n^2 is an integer.
(2) (rad n) is an integer.

My problem here is how would you know what to investigate for statement 2?

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Source: Beat The GMAT — Data Sufficiency | Sun Jun 07, 2015 10:58 pm

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Mon Jun 08, 2015 2:55 am

gamecomplete wrote:Is n an integer?

(1) n^2 is an integer.
(2) (rad n) is an integer.

My problem here is how would you know what to investigate for statement 2?

statement 2)
n^0.5 = x
(n^0.5)^2 = x^2
n = x^2
x = integer
integer x integer = integer
therefore n= integer
sufficent

statement 1)
n^2 = x
n = x^0.5
x can be any integer .... if x=2, n is not an integer
insufficent
ans = b

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 08, 2015 3:16 am

Is n an integer ?

(1) nÂ² is an integer

(2) âˆšn is an integer

Statement 1: nÂ² is an integer
Case 1: n=1, with the result that nÂ² = 1Â² = 1.
In this case, n is an integer.
Case 2: n=âˆš2, with the result that nÂ² = (âˆš2)Â² = 2.
In this case, n is NOT an integer.
INSUFFICIENT.

Statement 2: âˆšn is an integer
Since âˆšn = integer, n = (integer)Â².
In other words, n is a PERFECT SQUARE.
Thus, n is an integer.
SUFFICIENT.

The correct answer is B.

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Mon Jun 08, 2015 4:38 am

is rad n means n ^ 1/2 ?

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 08, 2015 5:44 am

nikhilgmat31 wrote:is rad n means n ^ 1/2 ?

Don't worry about that notation. On the actual GMAT, questions will feature square root symbols.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 08, 2015 9:54 am

Is n an integer ?

(1) nÂ² is an integer
(2) âˆšn is an integer

Concept/rule tested:
(integer)(integer) = integer

Similar concepts:
(integer) + (integer) = integer
(integer) - (integer) = integer

Target question: Is n an integer?

Statement 1: The median of the numbers is 30
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 3 (notice that 3Â² = 9, and 9 is an integer). In this case, n IS an integer
Case b: n = âˆš2 (notice that (âˆš2)Â² = 2, and 2 is an integer). In this case, n is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: âˆšn is an integer
If âˆšn is an integer, then n > 0
If n > 0, then (âˆšn)Â² = n
If âˆšn is an integer, we can write: (some integer)Â² = n
In other words, (some integer)(some integer) = n
By the above rule, n must be an integer.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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gmatbeater1989: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Wed Oct 07, 2015 12:04 pm

by gmatbeater1989 » Wed Oct 07, 2015 3:41 pm

gamecomplete wrote:Is n an integer?

(1) n^2 is an integer.
(2) (rad n) is an integer.

(1) n can be integer 1 or non-integer sqrt(2)
Insufficient

(2) sqrt(n) is integer.
n = sqrt(n) * sqrt(n)
So, n = integer * integer
n must be integer.

ANswer = B

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